Concentration Phenomena for The Nonlocal Schodinger Equation With Dirichlet Datum
Author
dc.contributor.author
Dávila Bonczos, Juan
Author
dc.contributor.author
Pino Manresa, Manuel del
Author
dc.contributor.author
Dipierro, Serena
Author
dc.contributor.author
Valdinoci, Enrico
Admission date
dc.date.accessioned
2015-12-23T02:05:26Z
Available date
dc.date.available
2015-12-23T02:05:26Z
Publication date
dc.date.issued
2015
Cita de ítem
dc.identifier.citation
Analysis & PDE Vol. 8, No. 5, 2015
en_US
Identifier
dc.identifier.issn
1948-206X
Identifier
dc.identifier.other
DOI: 10.2140/apde.2015.8.1165
Identifier
dc.identifier.uri
https://repositorio.uchile.cl/handle/2250/135929
General note
dc.description
Artículo de publicación ISI
en_US
Abstract
dc.description.abstract
For a smooth, bounded domain , s 2 .0; 1/, p 2 .1; .nC2s/=.n2s// we consider the nonlocal equation
"2s.1/su Cu D u p in
with zero Dirichlet datum and a small parameter " >0. We construct a family of solutions that concentrate
as "!0 at an interior point of the domain in the form of a scaling of the ground state in entire space.
Unlike the classical case s D 1, the leading order of the associated reduced energy functional in a
variational reduction procedure is of polynomial instead of exponential order on the distance from the
boundary, due to the nonlocal effect. Delicate analysis is needed to overcome the lack of localization, in
particular establishing the rather unexpected asymptotics for the Green function of "2s.1/s C1 in the
expanding domain "1 with zero exterior datum